Subgroups — C₂×D₅×C₃₁₁⋊C₅ #44527366

Order 31100.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₃₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₃₁₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	C₅×C₃₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₅×C₃₁₁	C₅	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃₁₁⋊C₅	—	5	1	no	maximal
6	C₂×C₅×C₃₁₁	C₂×C₅	1	1	yes	characteristic, complemented
7	D₅×C₃₁₁	C₂×C₅	1	2	yes	complemented
8	C₂×C₃₁₁⋊C₅	—	2	2	no	—
9	C₂×C₃₁₁⋊C₅	—	5	2	no	—
10	C₂×C₃₁₁⋊C₅	D₅	1	1	yes	characteristic, direct product factor
11	C₅×C₃₁₁	C₂²×C₅	1	1	yes	characteristic, complemented
12	C₃₁₁⋊C₅	—	2	2	no	—
13	C₃₁₁⋊C₅	C₂×D₅	1	1	yes	characteristic, direct product factor
14	C₂²×C₃₁₁	—	5	1	no	Hall
15	C₂×C₃₁₁	—	5	2	no	—
16	C₂×C₃₁₁	C₅×D₅	1	1	yes	characteristic, complemented
17	C₃₁₁	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅×D₅	—	311	1	no	maximal, Hall
19	C₂×C₅²	—	311	1	no	—
20	C₅×D₅	—	311	2	no	—
21	C₅²	—	311	1	no	Sylow
22	C₂²×C₅	—	1555	1	no	—
23	C₂×D₅	C₃₁₁⋊C₅	1	1	yes	characteristic, direct product factor
24	C₂×C₅	—	1555	2	no	—
25	C₂×C₅	—	311	1	no	—
26	C₂×C₅	—	622	2	no	—
27	C₂×C₅	C₂×C₃₁₁⋊C₅	1	1	yes	characteristic, complemented
28	D₅	C₂×C₃₁₁⋊C₅	1	2	yes	direct product factor
29	C₅	—	311	1	no	—
30	C₅	—	622	2	no	—
31	C₅	C₂²×C₃₁₁⋊C₅	1	1	yes	characteristic, complemented
32	C₂²	—	5	1	no	Sylow
33	C₂	—	5	2	no	—
34	C₂	D₅×C₃₁₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅×C₃₁₁⋊C₅
commutator, cosocle, hypocenter	C₅×C₃₁₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₃₁₁	C₂×C₅
LCS	G ▷ C₅×C₃₁₁
UCS	C₁ ◁ C₂

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₅×C₃₁₁⋊C₅	C₂	semidirect
2. D₅×C₃₁₁⋊C₅	C₂	direct (N × H)
3. C₅×C₃₁₁⋊C₅	C₂²	semidirect
4. C₂×D₅×C₃₁₁	C₅	semidirect
6. C₂×C₅×C₃₁₁	C₂×C₅	semidirect
7. D₅×C₃₁₁	C₂×C₅	semidirect
10. C₂×C₃₁₁⋊C₅	D₅	direct (N × H)
11. C₅×C₃₁₁	C₂²×C₅	semidirect
13. C₃₁₁⋊C₅	C₂×D₅	direct (N × H)
16. C₂×C₃₁₁	C₅×D₅	semidirect
17. C₃₁₁	C₂×C₅×D₅	semidirect
23. C₂×D₅	C₃₁₁⋊C₅	direct (N × H)
27. C₂×C₅	C₂×C₃₁₁⋊C₅	semidirect
28. D₅	C₂×C₃₁₁⋊C₅	direct (N × H)
31. C₅	C₂²×C₃₁₁⋊C₅	semidirect
34. C₂	D₅×C₃₁₁⋊C₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×C₃₁₁⋊C₅	2
D₅×C₃₁₁⋊C₅	2
C₂×D₅×C₃₁₁	5
C₂²×C₃₁₁⋊C₅	5
C₂×C₅×D₅	311

Subgroups — C2×D5×C311⋊C5 #44527366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₃₁₁⋊C₅ #44527366